Advertisement

Application of RELAX in Time Delay Estimation

  • Renbiao WuEmail author
  • Qiongqiong Jia
  • Lei Yang
  • Qing Feng
Chapter

Abstract

Suppose that we have a single sensor receiving a superposition of attenuated and delayed replicas of a known signal plus noise. The estimation of arrival times and amplitudes of various received signals from the received data is the well known time delay estimation problem, which occurs in radar, active sonar, wireless communication, nondestructive testing, geophysics, seismic exploration, medical imaging, and many others fields.

References

  1. 1.
    Stoica P, et al. Modern signal spectrum analysis. Trans. RB Wu, Beijing: Electronic Industry Press; 2012.Google Scholar
  2. 2.
    Padron I. Recent interferometry applications in topography and astronomy. Croatia: INTECH open access publisher; 2012.CrossRefGoogle Scholar
  3. 3.
    Li J, Wu RB. An efficient algorithm for time delay estimation. IEEE Trans Signal Process. 1998;46(8):2231–5.CrossRefGoogle Scholar
  4. 4.
    Wu RB, Li J. Time delay estimation via optimizing highly oscillatory cost functions. IEEE J Oceanic Eng. 1998;23(3):235–44.CrossRefGoogle Scholar
  5. 5.
    Wu RB, Li J, Liu ZS. Super resolution time delay estimation via MODE-WRELAX. IEEE Trans Aerosp Electron Syst. 1999;35(1):294–307.CrossRefGoogle Scholar
  6. 6.
    Li J, Wu RB, Liu ZS. Efficient super resolution time delay estimation techniques. IEEE Int Conf Acoust Speech Signal Process. 1998;4(4):2473–6.Google Scholar
  7. 7.
    Wu RB, Li J. Time delay estimation with multiple looks in colored noise. IEEE Trans Aerosp Electron Syst. 1999;35(4):1354–61.CrossRefGoogle Scholar
  8. 8.
    Wu RB, Li X, Li J. Continous pavement profiling with ground penetrating radar. IEEE Proc Radar Sonar Navig. 2002;149(4):183–93.CrossRefGoogle Scholar
  9. 9.
    Wu RB, Li J. Novel time delay estimation methods with applications to ultra wideband ground penetrating radar. Proc of SPIE. 1998;57–68.Google Scholar
  10. 10.
    Su ZG, Wu RB. Delay and doppler scale estimation of multiple moving targets via DS-WRELAX. Electron Lett. 2000;36(9):827–8.CrossRefGoogle Scholar
  11. 11.
    Su ZG, Wu RB, Yu JP. Further results on the DS-WRELAX algorithm for the delay and doppler scale estimation of multiple moving targets. In: 5th International conference on signal processing proceedings; 2000. p. 201–5.Google Scholar
  12. 12.
    Su ZG. Studies on effective algorithm of multi-objective parameter estimation based on decoupled parameter estimation theory. Nanjing: Master Thesis of Nanjing University of Aeronautics and Astronautics; 2000.Google Scholar
  13. 13.
    Ehrenberg JE, Ewatt TE, Morris RD. Signal processing techniques for resolving individual pulses in multipath signal. J Acoust Soc Am. 1978;63(6):1861–5.CrossRefGoogle Scholar
  14. 14.
    Bian YI, Last D. Eigen-decomposition techniques for Loran-C skywave estimation [J]. IEEE Trans Aerosp Electron Syst. 1997;33(1):117–24.CrossRefGoogle Scholar
  15. 15.
    Kirsteins I. High-resolution time delay estimation. IEEE Trans Acoust Speech Signal Proc (ASSP). 1987;12:451–4.Google Scholar
  16. 16.
    Kirsteins IP, Kot AC. Performance analysis of a high resolution time delay estimation algorithm. IEEE Trans Acoust Speech Signal Proc (ASSP). 1990;(5):2767–70.Google Scholar
  17. 17.
    Feder M, Weinstein E. Parameter estimation of superimposed signals using the EM algorithm. IEEE Trans Acoust Speech Signal Proc (ASSP). 1988;36(4):477–89.Google Scholar
  18. 18.
    Li X, Wu RB, Rasmi S, et al. An acoustic proximity ranging system for monitoring the cavity thickness. IEEE Trans Ultrason. 2003;50(7):898–910.CrossRefGoogle Scholar
  19. 19.
    Li X, Wu RB, Rasmi S, et al. Acoustic proximity ranging in the presence of secondary echoes. IEEE Trans Instrum Meas. 2003;52(5):1593–605.CrossRefGoogle Scholar
  20. 20.
    Li X, Wu RB, Sheplak M, et al. Multifrequency CW-based time-delay estimation for proximity ultrasonic sensors. IEEE Proc Radar Sonar Navig. 2002;149(2):53–9.CrossRefGoogle Scholar
  21. 21.
    Wu RB, Wang WY, Lu D, el al. Adaptive interference mitigation in GNSS. Beijing: Science Press; 2015.Google Scholar
  22. 22.
    Li J. Studies on several key InteReference Mitigation techniques in GNSS. Tianjin: PhD Dissertation of Tianjin University; 2013.Google Scholar
  23. 23.
    Wu RB, Li J, Wang WY, Lu D, Wang L. Multipath interference mitigation in GNSS based on decoupled parameter estimation theory. China: ZL201110327356.2, 2013.10.30.Google Scholar
  24. 24.
    Mohammed S. Fourier transform—signal processing and physical sciences. Croatia: INTECH Open Access Publisher; 2015.Google Scholar
  25. 25.
    Jia QQ, Wu RB, Wang WY, et al. Multipath interference mitigation in GNSS via WRELAX. GPS Solutions. 2017;21(2):487–98.CrossRefGoogle Scholar
  26. 26.
    Li J, Wu RB, Wang WY, et al. GPS fine time delay estimation based on signal separation estimation theory. In: 2012 IEEE 11th international conference on signal processing; 2012. p. 236–40.Google Scholar
  27. 27.
    Li J, Wu RB, Wang WY, et al. A novel GPS signal acquisition algorithm. Adv Inf Sci Serv Sci. 2012;4(17):597–604.Google Scholar
  28. 28.
    Wu RB, Li J. Adaptive ground bounce removal for landmine detection with ground penetrating radar. Electron Lett. 2001;37(20):1250–2.CrossRefGoogle Scholar
  29. 29.
    Manickam TG, Vaccaro RG, Tufts DW. A least-squares algorithm for multipath-time-delay estimation. IEEE Trans Signal Process. 1994;42(11):3229–33.CrossRefGoogle Scholar
  30. 30.
    Schmidt R. Multiple emitter location and signal parameter estimation. IEEE Trans Antennas Propag. 1986;34(3):276–80.CrossRefGoogle Scholar
  31. 31.
    Roy R, Paulraj A, Kailath T. Esprit-a subspace rotation approach to estimation of parameters of cisoids in noise. IEEE Trans Acoust Speech Signal Proc (ASSP). 1986;34(5):1340–2.CrossRefGoogle Scholar
  32. 32.
    Kay SM. Modern spectral estimation: theory and application. New Jersey: Prentice-Hall; 1988.zbMATHGoogle Scholar
  33. 33.
    Li J, Stoica P. Efficient mixed-spectrum estimation with applications to target feature extraction [J]. IEEE Trans Signal Process. 1996;44(2):281–95.CrossRefGoogle Scholar
  34. 34.
    Carter GC. Coherence and time delay estimation. Proc IEEE. 1987;75(2):236–55.CrossRefGoogle Scholar
  35. 35.
    Chan Y, Riley J, Plant J. A parameter estimation approach to time-delay estimation and signal detection. IEEE Trans Acoust Speech Signal Process (ASSP). 1980;28(1):8–16.zbMATHCrossRefGoogle Scholar
  36. 36.
    Bell B, Ewart T. Separating multipaths by global optimization of multidimensional matched filter. IEEE Trans Acoust Speech Signal Process (ASSP). 1986;34(5):1029–37.CrossRefGoogle Scholar
  37. 37.
    Tremblay R, Carter G, Lytle D. A practical approach to the estimation of amplitude and time-delay parameters of a composite signal. IEEE J Oceanic Eng. 1987;12(1):273–8.CrossRefGoogle Scholar
  38. 38.
    Vaccaro RJ, Ramalingam CS, Tufts DW, et al. Least-squares time-delay estimation for transient signals in a multipath environment. J Acoust Soc Am. 1992;92(1):210–8.CrossRefGoogle Scholar
  39. 39.
    Blackowiak AD, Rajan SD. Multipath arrival estimates using simulated annealing: application to crosshole tomography experiment. IEEE J Oceanic Eng. 1995;20(3):157–65.CrossRefGoogle Scholar
  40. 40.
    Tremblay RJ, Lytle DW. Development and analysis of echo classification using time delays [J]. IEEE J Oceanic Eng. 1996;21(2):205–15.CrossRefGoogle Scholar
  41. 41.
    Tufts DW, Kumaresan R, Kirsteins I. Data adaptive signal estimation by singular value decomposition of a data matrix. Proc IEEE. 1982;70(6):684–5.CrossRefGoogle Scholar
  42. 42.
    Moon TK. The expectation-maximization algorithm. IEEE Signal Process Mag. 1996;13(6):47–60.CrossRefGoogle Scholar
  43. 43.
    Officer CB. Introduction to the theory of sound transmission. Phys Today. 1958;12:66.MathSciNetCrossRefGoogle Scholar
  44. 44.
    Soderstrom T, Stoica P. System identification. New Jersey: Prentice-Hall; 1988.zbMATHGoogle Scholar
  45. 45.
    Stoica P, Soderstrom T. On reparametrization of loss functions used in estimation and the invariance principle. Sig Process. 1989;17(4):383–7.MathSciNetCrossRefGoogle Scholar
  46. 46.
    Bruckstein AM, Shan TJ, Kailath T. The resolution of overlapping echoes. IEEE Trans Acoust Speech Signal Process (ASSP). 1986;33(6):1357–67.CrossRefGoogle Scholar
  47. 47.
    Stoica P, Moses RL. Introduction to spectral analysis. New Jersey: Prentice-Hall; 1997.zbMATHGoogle Scholar
  48. 48.
    Stewart GW. Introduction to matrix computations. Amsterdam: Elsevier; 1973.zbMATHGoogle Scholar
  49. 49.
    Zangwill WI. Nonlinear programming: a unified approach. New Jersey: Prentice-Hall; 1967.zbMATHGoogle Scholar
  50. 50.
    Zehna PW. Invariance of maximum likelihood estimation. Annu Math Stat. 1966;37(3):744.Google Scholar
  51. 51.
    Kirsteins IP, Quazi A. Exact maximum likelihood time delay estimation for deterministic signals. In: proceedings of EURASIP 1988; 1988. p. 531–4.Google Scholar
  52. 52.
    Minoux M. Programmation mathematique theorie et algorithmes, Paris: Dunod; 1977.Google Scholar
  53. 53.
    Stoica P, Sharman KC. Novel eigenanalysis method for direction estimation. IEEE proc F-Radar Signal Process. 1990;137(1):19–26.MathSciNetCrossRefGoogle Scholar
  54. 54.
    Stoica P, Sharman KC. Maximum likelihood methods for direction-of-arrival estimation. IEEE Trans Acoust Speech Signal Process (ASSP). 1990;38(7):1132–43.zbMATHCrossRefGoogle Scholar
  55. 55.
    Golub GH, van Loan CF. Matrix computations. Maryland: Johns Hopkins University Press; 1989.zbMATHGoogle Scholar
  56. 56.
    Jakowatz CV, Wahl DE, Eichel PH, et al. Spotlight-mode synthetic aperture radar: a signal processing approach. New York: Springer; 2012.Google Scholar
  57. 57.
    Williams DB, Johnson DH. Robust estimation of structured covariance matrices. IEEE Trans Signal Process. 1993;41(9):2891–906.zbMATHCrossRefGoogle Scholar
  58. 58.
    Li H, Stoica P, Li J. Computationally efficient maximum-likelihood estimation of structured covariance matrices. IEEE Trans Signal Process. 1999;47(5):1314–23.MathSciNetzbMATHCrossRefGoogle Scholar
  59. 59.
    Bangs WJ. Array processing with generalized beam-formers, New Haven: PhD Dissertation of Yale University; 1971.Google Scholar

Copyright information

© Science Press, Beijing and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Renbiao Wu
    • 1
    Email author
  • Qiongqiong Jia
    • 1
  • Lei Yang
    • 1
  • Qing Feng
    • 1
  1. 1.Tianjin Key Lab for Advanced Signal ProcessingCivil Aviation University of ChinaTianjinChina

Personalised recommendations